We study the competition between Kondo physics and indirect exchange on monolayer black phosphorous using a realistic description of the band structure in combination with the density matrix renormalization group (DMRG) method. The Hamiltonian is reduced to a one-dimensional problem via an exact canonical transformation that makes it amenable to DMRG calculations, yielding exact results that fully incorporate the many-body physics. We find that a perturbative description of the problem is not appropriate and cannot account for the slow decay of the correlations and the complete lack of ferromagnetism. In addition, at some particular distances, the impurities decouple forming their own independent Kondo states. This can be predicted from the nodes of the Lindhard function. Our results indicate a possible route toward realizing dilute anti-ferromagnetism in phosphorene.